Embedded-width: A variant of treewidth for plane graphs
Discrete Mathematics
2017-03-23 v1
Abstract
We define a special case of tree decompositions for planar graphs that respect a given embedding of the graph. We study the analogous width of the resulting decomposition we call the embedded-width of a plane graph. We show both upper bounds and lower bounds for the embedded-width of a graph in terms of its treewidth and describe a fixed parameter tractable algorithm to calculate the embedded-width of a plane graph. To do so, we give novel bounds on the size of matchings in planar graphs.
Cite
@article{arxiv.1703.07532,
title = {Embedded-width: A variant of treewidth for plane graphs},
author = {Glencora Borradaile and Jeff Erickson and Hung Le and Robbie Weber},
journal= {arXiv preprint arXiv:1703.07532},
year = {2017}
}